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ENDOXA

Curie´s Principle and Indeterminism

José Luis Rolleri

Published Dec 23, 2020• 0 citations
Publisher

Abstract

Curiés principle expresses an invariant connectiobn between symmetry of causes and symmetry of effects in deterministic systems. Here a probabilistic version of such principle is proposed and proved for indeterministic systems. In contrast with Curie´s principle, our probabilistic version involves the invariance of the probabilities that laws assign to physically possible final states of random processes under symmetry transformations, although with exceptions when a phenomenon breaks the symmetry in question.

DOI
10.5944/endoxa.46.2020.23677

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Curiés principle expresses an invariant connectiobn between symmetry of causes and symmetry of effects in deterministic systems. Here a probabilistic version of such principle is proposed and proved for indeterministic systems. In contrast with Curie´s principle, our probabilistic version involves the invariance of the probabilities that laws assign to physically possible final states of random processes under symmetry transformations, although with exceptions when a phenomenon breaks the symmetry in question.
This essay explores the nature of spontaneous symmetry breaking (SSB) in connection with a cluster of interrelated concepts such as Curie's symmetry principle, ergodicity, and chance and stability in classical systems. First, a clarification of the two existing senses of SSB is provided and an argument developed for a proposal for SSB, in which not only the possibilities but also the actual breakings are referred to. Second, a detailed analysis is given of classical SSB that answers the questions: (i) how we are justified in regarding it as a matter of chance, and (ii) why the breakings in it are equally probable. The answer provides some support to the applicability of ergodicity in special systems (such as ours).
This article focuses on three themes concerning determinism and indeterminism. The first is observational equivalence between deterministic and indeterministic models. The article discusses several results about observational equivalence and presents an argument on how to choose between deterministic and indeterministic models involving indirect evidence. The second is whether Newtonian physics is indeterministic. The article argues that the answer depends on what one takes Newtonian mechanics to be and highlights how contemporary debates on this issue differ from those in the nineteenth century. The third theme is how the method of arbitrary functions can be used to make sense of deterministic probabilities. The article discusses various ways of interpreting the initial probability distributions and argues that they are best understood as physical, biological, and other quantities characterizing the particular situation. The fact that the method of arbitrary functions deserves more attention than it has received so far is also emphasized.
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This paper argues that such strictly deterministic formulations rely on idealizations that obscure an essential physical feature: the objective growth of information associated with irreversible processes. Drawing on thermodynamics, information theory, and the foundations of quantum mechanics, the paper is based on the notion of ontic entropy as a measure of the objective informational content instantiated by physical systems. This paper proposes a classification of determinism based on the informational characteristics of physical evolution. By distinguishing between strict causal determinism, probabilistic determinism, and chaotic determinism, it becomes possible to analyze causal structure without conflating necessity with lawfulness or probability with indeterminism.
By Invoking symmetry principle, we present a self-consistent interpretation of the existing quantum theory which explains why our world is fundamentally indeterministic and that why non-local quantum jumps occur. Symmetry principle dictates that the concept of probability is more fundamental than the notion of the wave function in that the former can be derived directly from symmetries rather than have to be assumed as an additional axiom. It is argued that the notion of quantum probability and that of the wavefunction are intimately connected.
Abstract Is the world deterministic and can we ever know whether it is or is not so? This chapter critically evaluates recent results that bear on these issues, and points out the relation to probabilities. While results from classical physics are neither fully relevant nor conclusive, quantum mechanics is often assumed to establish indeterminism beyond doubt. However, whether the quantum world is indeterministic crucially depends on how the measurement problem is solved. There are both deterministic and indeterministic contenders in this field, some of them empirically equivalent to another one. This is shown using the deterministic Bohm theory and Nelsonsion mechanics, which is indeterministic. Two arguments that purport to establish indeterminism and that rely on Gleason's theorem and on Conway and Kochen's recent Free Will Theorem are shown to be wanting.